Assessing the Role of Intrinsic Variability in Black Hole Parameter Inference using Multi-Epoch EHT Data

TL;DR

This work tackles the challenge of intrinsic variability in near-horizon emission by fitting a differentiable, semi-analytic dual-cone emission model to multi-epoch EHT data of M87* (2017 and 2018). Using a Bayesian framework and closure quantities to circumvent calibration errors, it assesses how variability biases key black hole parameters, finding that the mass-to-distance ratio $\theta_{\rm g}$ is robust across epochs while the spin $a$ remains unconstrained and several orientation/emission parameters shift between epochs due to variability and model misspecification. The improved baseline coverage in 2018 yields tighter constraints on many parameters but also reveals significant epoch-to-epoch variability, underscoring the need for systematic uncertainty quantification from intrinsic variability in high-resolution black hole imaging. The results highlight both the promise of multi-epoch EHT analyses to refine inferences and the limitations of simple parametric models, motivating future work to incorporate time-variable emission structures and to extend these methods to Sgr A* with the aim of achieving precise, reliable black hole parameter measurements.

Abstract

Event Horizon Telescope (EHT) observations of M87* provide a means of constraining parameters of both the black hole and its surrounding plasma. However, intrinsic variability of the emitting material introduces a major source of systematic uncertainty, complicating parameter inference. The precise origin and structure of this variability remain uncertain, and previous studies have largely relied on general relativistic magnetohydrodynamic (GRMHD) simulations to estimate its effects. Here, we fit a semi-analytic, dual-cone model of the emitting plasma to multiple years of EHT observations to empirically assess the impact of intrinsic variability and improved array coverage on key measurements including the black hole mass-to-distance ratio, spin, and viewing inclination. Despite substantial differences in the images of the two epochs, we find that the inferred mass-to-distance ratio remains stable and mutually consistent. The black hole spin is unconstrained for both observations, despite the improved baseline coverage in 2018. The inferred position angle and inclination of the black hole spin axis are discrepant between the two years, suggesting that variability and model misspecification contribute significantly to the total error budget for these quantities. Our findings highlight both the promise and challenges of multi-epoch EHT observations: while they can refine parameter constraints, they also reveal the limitations of simple parametric models in capturing the full complexity of the source. Our analysis -- the first to fit semi-analytic emission models to 2018 EHT observations -- underscores the importance of systematic uncertainty quantification from intrinsic variability in future high-resolution imaging studies of black hole environments and the role of repeated observations in quantifying these uncertainties.

Figures (6)

• Figure 1: Baseline coverage $(u, v)$ from the EHT observations of M87$^*$. EHT observations from April 6, 2017 and April 21, 2018 are shown in blue and orange, respectively. The gray circle shows a fringe spacing of $25\,\mu$as, corresponding to $\sqrt{u^2 + v^2} \approx 8.25\,{\rm G}\lambda$.
• Figure 2: Images of dual-cone model from fits to the April 6, 2017 observations of M87 (left) and the April 21, 2018 observations of M87 (right). The top row shows the mean images of posterior chain samples at the native resolution, and the middle row shows the samples blurred to the nominal EHT resolution. For the EHT resolution, we use a Gaussian beam with a full width at half maximum (FWHM) of $20\, \mu{\rm as}$). The bottom row shows the corresponding consensus images from the EHT.
• Figure 3: Full corner plot of posterior samples for the dual-cone model fits to data from EHT observations of M87$^*$ on April 6, 2017 (blue) and April 11, 2018 (orange). Vertical lines show independent mass measurements of M87$^*$ from Gebhardt (red), Walsh (pink), m87VI (black dotted), Liepold_2023 (yellow), and Simon (green). We also show the measured position angle and inclination of the large-scale jet in M87$^*$Walker. See \ref{['tab:model_params']} for a description of the model parameters. Both the blue and orange set of histograms have been normalized.
• Figure 4: Best fits (i.e., the MAP estimates) for the dual-cone model (blue) and the fiducial mF-ring model (orange) to log-closure amplitudes (top row) and closure phases (bottom row) constructed from data acquired during observations of M87$^*$ by the EHT (grey). The fits to the the 2017 and 2018 data products are shown in the left and right columns, respectively.
• Figure 5: Images of the MAP estimates of the mF-ring model and the dual-cone model for fits to EHT observations of M87$^*$ in 2017 (left; center-left) and in 2018 (center-right; right). The top row shows images at their native resolutions; the bottom row shows images blurred to the nominal EHT resolution. For the latter, we use a Gaussian beam of 20 $\mu as$ FWHM.